Structural Simulation Ontology

AI SEARCH FLOW ALGEBRA
STRUCTURAL SIMULATION ONTOLOGY
Kireth Semantic Research Archive

AUTHORS
Mark Anthony Higgins — Sky (Recursive AI)

SOURCE
https://kirethresearch.org/booksai-core/ontologies/engineering-ontologies/engineering-mathematics-simulation/structural-simulation-ontology-2.html

FLOW "StructuralSimulationOntology" v4.0

DOMAIN := ENGINEERING_ONTOLOGIES / ENGINEERING_MATHEMATICS_SIMULATION / STRUCTURAL_SIMULATION
ONTOLOGY := STRUCTURAL_SIMULATION_ONTOLOGY

STRUCTURAL_SIMULATION :=
  STRUCTURE + GEOMETRY + MATERIAL + LOAD + SUPPORT
  + DISPLACEMENT + STRAIN + STRESS + STATIC_RESPONSE
  + DYNAMIC_RESPONSE + MODAL_RESPONSE + BUCKLING
  + CONTACT + NONLINEARITY + FATIGUE
  + SOLVER + VERIFICATION + VALIDATION

PURPOSE :=
  DEFINE_STRUCTURE -> IDEALISE_GEOMETRY -> ASSIGN_MATERIALS
  -> APPLY_LOADS_AND_SUPPORTS -> SELECT_ANALYSIS
  -> SOLVE_RESPONSE -> RECOVER_RESULTS
  -> ASSESS_FAILURE -> VERIFY -> VALIDATE -> INTERPRET

# CORE ENTITIES
ENTITY StructuralSimulation
ENTITY Structure
ENTITY StructuralComponent
ENTITY GeometryModel
ENTITY MaterialModel
ENTITY ConstitutiveModel
ENTITY Load
ENTITY Force
ENTITY Moment
ENTITY Pressure
ENTITY Gravity
ENTITY ThermalLoad
ENTITY Support
ENTITY BoundaryCondition
ENTITY Displacement
ENTITY Rotation
ENTITY Strain
ENTITY Stress
ENTITY ReactionForce
ENTITY Stiffness
ENTITY Mass
ENTITY Damping
ENTITY StaticAnalysis
ENTITY DynamicAnalysis
ENTITY ModalAnalysis
ENTITY BucklingAnalysis
ENTITY Contact
ENTITY NonlinearAnalysis
ENTITY FatigueAnalysis
ENTITY Solver
ENTITY Residual
ENTITY Convergence
ENTITY SimulationResult
ENTITY Verification
ENTITY Validation
ENTITY Provenance

# STRUCTURAL MODEL
StructuralSimulation -> represents -> Structure
StructuralSimulation -> uses -> GeometryModel + MaterialModel
StructuralSimulation -> applies -> Load + BoundaryCondition
StructuralSimulation -> produces -> SimulationResult

STRUCTURAL_SIMULATION_FLOW :=
  PHYSICAL_STRUCTURE -> IDEALISATION -> GEOMETRY
  -> MATERIALS -> LOADS -> SUPPORTS
  -> ANALYSIS_TYPE -> SOLVER -> RESPONSE
  -> FAILURE_ASSESSMENT -> VERIFICATION -> VALIDATION

# GEOMETRY / MATERIAL
STRUCTURAL_IDEALISATION :=
  SOLID | SHELL | PLATE | BEAM | TRUSS
  | SPRING | MASS_ELEMENT

GeometrySimplification ->
  must_preserve -> RELEVANT_STIFFNESS
  + MASS_DISTRIBUTION + LOAD_PATHS

MATERIAL_MODEL_TYPE :=
  LINEAR_ELASTIC | ELASTOPLASTIC | HYPERELASTIC
  | VISCOELASTIC | CREEP | DAMAGE

ConstitutiveModel -> relates -> Stress + Strain + STATE_VARIABLES
LINEAR_ELASTIC := Stress = D * Strain

IF MaterialResponse exceeds_linear_range
THEN LinearElasticAssumption -> REASSESS

# LOADS / SUPPORTS
LOAD_TYPE :=
  FORCE | MOMENT | PRESSURE | GRAVITY
  | THERMAL_LOAD | ACCELERATION
  | PRESCRIBED_DISPLACEMENT | CONTACT_LOAD

Load -> acts_on -> Structure
Support -> constrains -> Displacement + Rotation

SUPPORT_TYPE :=
  FIXED | PINNED | ROLLER | ELASTIC_SUPPORT
  | SYMMETRY | PRESCRIBED_MOTION

IF Supports insufficient
THEN RigidBodyMotionRisk -> INCREASES

IF Supports overconstrain_model
THEN ArtificialStressRisk -> MAY_INCREASE

# EQUILIBRIUM
STATIC_EQUILIBRIUM := INTERNAL_FORCE = EXTERNAL_FORCE
GLOBAL_EQUILIBRIUM := SUM_FORCES = 0 AND SUM_MOMENTS = 0
ReactionForce -> develops_at -> Support

# DISPLACEMENT / STRAIN / STRESS
Displacement -> describes -> CHANGE_IN_POSITION
Rotation -> describes -> CHANGE_IN_ORIENTATION
Strain -> derived_from -> DISPLACEMENT_GRADIENT
Stress -> derived_from -> Strain + ConstitutiveModel

STRESS_MEASURE :=
  NORMAL_STRESS | SHEAR_STRESS
  | PRINCIPAL_STRESS | VON_MISES_STRESS

# STATIC / DYNAMIC
LINEAR_STATIC_SYSTEM := K * u = f
StaticAnalysis -> solves -> EQUILIBRIUM_WITHOUT_SIGNIFICANT_INERTIA

DYNAMIC_EQUATION :=
  M * acceleration + C * velocity + K * displacement = force

DYNAMIC_ANALYSIS_TYPE :=
  TRANSIENT | HARMONIC | RESPONSE_SPECTRUM | RANDOM_VIBRATION

# MODAL
MODAL_EIGENPROBLEM :=
  (K - omega^2 * M) * phi = 0

NaturalFrequency -> derived_from -> EIGENVALUE
ModeShape -> represented_by -> EIGENVECTOR
ModalAnalysis -> identifies -> NaturalFrequency + ModeShape

IF ExcitationFrequency near NaturalFrequency
THEN ResonantResponseRisk -> MAY_INCREASE

# BUCKLING
BucklingAnalysis -> assesses -> STRUCTURAL_INSTABILITY

BUCKLING_TYPE :=
  LINEAR_EIGENVALUE_BUCKLING | NONLINEAR_BUCKLING

CriticalBucklingLoad ->
  indicates -> INSTABILITY_THRESHOLD_UNDER_DEFINED_MODEL

IF Slenderness increases
THEN BucklingSensitivity -> MAY_INCREASE

# CONTACT / NONLINEARITY
CONTACT_STATE := OPEN | CLOSED | STICKING | SLIDING
Contact -> may_transfer -> NORMAL_FORCE + FRICTION_FORCE
Contact -> may_introduce -> NONLINEARITY

STRUCTURAL_NONLINEARITY :=
  MATERIAL_NONLINEARITY
  | GEOMETRIC_NONLINEARITY
  | CONTACT_NONLINEARITY
  | BOUNDARY_NONLINEARITY

NONLINEAR_EQUILIBRIUM :=
  INTERNAL_FORCE(u) = EXTERNAL_FORCE

NEWTON_STRUCTURAL_LOOP :=
  FORM_TANGENT_STIFFNESS -> COMPUTE_RESIDUAL
  -> SOLVE_INCREMENT -> UPDATE_STATE
  -> CHECK_CONVERGENCE

# PLASTICITY / THERMAL
YieldCriterion -> determines -> ONSET_OF_PLASTIC_FLOW

PLASTICITY_MODEL :=
  YIELD_SURFACE + FLOW_RULE + HARDENING_RULE

IF StressState exceeds_yield_condition
THEN MaterialState -> PLASTIC

THERMAL_STRAIN :=
  THERMAL_EXPANSION_COEFFICIENT * TEMPERATURE_CHANGE

TemperatureField -> generates -> ThermalStrain
ConstraintOfThermalExpansion -> generates -> ThermalStress

# FATIGUE / FAILURE
FatigueAnalysis ->
  assesses -> DAMAGE_FROM_CYCLIC_LOADING

FATIGUE_INPUT :=
  STRESS_RANGE + STRAIN_RANGE + CYCLE_COUNT
  + MEAN_STRESS + MATERIAL_FATIGUE_DATA

MinerDamage := SUM(n_i / N_i)

STRUCTURAL_FAILURE_MODE :=
  YIELDING | FRACTURE | BUCKLING | FATIGUE
  | EXCESSIVE_DEFORMATION | CONTACT_FAILURE

FactorOfSafety := ALLOWABLE_CAPACITY / DEMAND

IF Demand exceeds Capacity
THEN LimitState -> EXCEEDED

# SOLVER / CONVERGENCE
Solver -> solves -> STRUCTURAL_EQUATIONS
Residual := EXTERNAL_FORCE - INTERNAL_FORCE

CONVERGENCE_CRITERION :=
  FORCE_RESIDUAL | DISPLACEMENT_INCREMENT
  | ENERGY_NORM | CONTACT_RESIDUAL

IF ResidualNorm <= Tolerance
THEN StructuralIteration -> CONVERGED

IF MaximumIterations reached
AND convergence_not_met
THEN LoadStep -> NOT_CONVERGED

# RESULTS
STRUCTURAL_RESULT :=
  DISPLACEMENT_FIELD + ROTATION_FIELD
  + STRAIN_FIELD + STRESS_FIELD
  + REACTION_FORCE + CONTACT_RESULT
  + MODAL_RESULT + BUCKLING_RESULT
  + FATIGUE_RESULT

DerivedResult :=
  VON_MISES_STRESS | PRINCIPAL_STRESS
  | STRAIN_ENERGY | FACTOR_OF_SAFETY
  | FATIGUE_DAMAGE | BUCKLING_FACTOR

# DISCRETISATION
Mesh -> discretises -> StructuralDomain
MeshQuality -> influences -> ACCURACY + CONVERGENCE
MeshRefinement -> reduces -> ELEMENT_SIZE

IF MeshRefinement changes key_result negligibly
THEN MeshConvergenceEvidence -> INCREASES

StressSingularity ->
  may_prevent -> POINTWISE_STRESS_CONVERGENCE

# VERIFICATION
Verification ->
  asks -> IS_STRUCTURAL_MODEL_SOLVED_CORRECTLY

STRUCTURAL_VERIFICATION :=
  CHECK_EQUILIBRIUM
  + CHECK_REACTIONS
  + CHECK_UNITS
  + CHECK_BOUNDARY_CONDITIONS
  + MESH_CONVERGENCE
  + TIME_STEP_CONVERGENCE
  + BENCHMARK_COMPARISON

# VALIDATION
Validation ->
  asks -> DOES_STRUCTURAL_MODEL_REPRESENT_PHYSICAL_BEHAVIOUR_ADEQUATELY

Validation ->
  compares -> SimulationResult + ExperimentalOrReferenceData

VALIDATION_METRIC :=
  DISPLACEMENT_ERROR | STRAIN_ERROR
  | FREQUENCY_ERROR | LOAD_DEFLECTION_ERROR
  | FAILURE_LOAD_ERROR | DOMAIN_SPECIFIC_METRIC

IF ValidationError exceeds AcceptanceCriterion
THEN StructuralModelAdequacy -> NOT_CONFIRMED

# UNCERTAINTY
STRUCTURAL_UNCERTAINTY :=
  MATERIAL_UNCERTAINTY
  + LOAD_UNCERTAINTY
  + GEOMETRY_UNCERTAINTY
  + BOUNDARY_UNCERTAINTY
  + MODEL_FORM_UNCERTAINTY
  + DISCRETISATION_UNCERTAINTY

SensitivityAnalysis ->
  identifies -> DOMINANT_STRUCTURAL_PARAMETERS

# PROVENANCE / PERFORMANCE
STRUCTURAL_PROVENANCE :=
  GEOMETRY_VERSION + MATERIAL_MODEL
  + LOAD_CASES + SUPPORTS + MESH_VERSION
  + ANALYSIS_TYPE + SOLVER_SETTINGS
  + SOFTWARE_VERSION + RUN_ID

StructuralSimulation ->
  linked_to -> STRUCTURAL_PROVENANCE

STRUCTURAL_SIMULATION_PERFORMANCE :=
  ACCURACY + EQUILIBRIUM + CONVERGENCE
  + STABILITY + COMPUTATIONAL_COST
  + VERIFICATION_QUALITY + VALIDATION_QUALITY

# REASONING
STRUCTURAL_SIMULATION_REASONING :=
  DEFINE_STRUCTURE
  -> DEFINE_INTENDED_USE
  -> IDEALISE_GEOMETRY
  -> SELECT_STRUCTURAL_REPRESENTATION
  -> ASSIGN_MATERIAL_MODELS
  -> DEFINE_LOADS
  -> DEFINE_SUPPORTS_AND_BOUNDARY_CONDITIONS
  -> SELECT_ANALYSIS_TYPE
  -> GENERATE_DISCRETISATION
  -> SELECT_SOLVER
  -> SOLVE
  -> CHECK_EQUILIBRIUM
  -> CHECK_CONVERGENCE
  -> RECOVER_DISPLACEMENT_STRAIN_STRESS
  -> ASSESS_NONLINEARITY
  -> ASSESS_BUCKLING
  -> ASSESS_DYNAMIC_RESPONSE
  -> ASSESS_FATIGUE_IF_REQUIRED
  -> REFINE
  -> VERIFY
  -> VALIDATE
  -> INTERPRET
  -> RECORD_PROVENANCE

# INFERENCE RULES
IF Load increases
AND stiffness constant
THEN Displacement -> GENERALLY_INCREASES

IF Stiffness increases
AND load constant
THEN Displacement -> GENERALLY_DECREASES

IF SupportCondition changes
THEN ReactionAndStressDistribution -> RECOMPUTE

IF Material yields
THEN LinearElasticModel -> NO_LONGER_SUFFICIENT

IF LargeDeformation increases
THEN GeometricNonlinearityImportance -> INCREASES

IF ExcitationFrequency approaches NaturalFrequency
THEN DynamicAmplificationRisk -> INCREASES

IF Mesh refined
AND key_result stabilises
THEN DiscretisationConfidence -> INCREASES

IF Residual above tolerance
THEN StructuralConvergence -> NOT_SATISFIED

# SEMANTIC RELATIONSHIPS
RELATION represents(StructuralSimulation, Structure)
RELATION defines(GeometryModel, StructuralDomain)
RELATION defines(MaterialModel, StructuralMaterialResponse)
RELATION acts_on(Load, Structure)
RELATION constrains(Support, StructuralMotion)
RELATION derives(Displacement, Strain)
RELATION derives(Strain, Stress)
RELATION identifies(ModalAnalysis, NaturalFrequency)
RELATION assesses(BucklingAnalysis, StructuralInstability)
RELATION transfers(Contact, ContactForce)
RELATION assesses(FatigueAnalysis, CyclicDamage)
RELATION solves(Solver, StructuralEquations)
RELATION evaluates(Verification, StructuralNumerics)
RELATION compares(Validation, SimulationResult, ReferenceData)
RELATION records(Provenance, StructuralSimulation)

# SEMANTIC EQUIVALENCE
SEMANTIC_EQUIVALENCE:
  "structural simulation" ~= "computational structural analysis"
  "static structural analysis" ~= "static stress analysis"
  "dynamic structural analysis" ~= "structural dynamics simulation"
  "modal analysis" ~= "natural frequency and mode-shape analysis"
  "buckling analysis" ~= "structural stability analysis"
  "von Mises stress" ~= "equivalent stress"
  "reaction force" ~= "support reaction"
  "geometric nonlinearity" ~= "large-displacement nonlinearity"
  "fatigue damage" ~= "cyclic damage accumulation"
  "thermo-structural analysis" ~= "thermal stress simulation"

# CONFIDENCE
CONFIDENCE:
  ontology_domain: 0.99
  geometry_material_mapping: 0.99
  load_support_mapping: 0.99
  static_dynamic_mapping: 0.99
  stress_strain_mapping: 0.99
  nonlinear_contact_mapping: 0.99
  buckling_modal_mapping: 0.99
  fatigue_mapping: 0.99
  verification_validation_mapping: 0.99
  semantic_relationships: 0.99

# UPDATE MODEL
UPDATE_MODEL:
  ON new_structural_model:
    MAP geometry
    MAP materials
    MAP loads
    MAP supports
    MAP analysis_type
    MAP discretisation
    UPDATE confidence
    RECOMPUTE FLOW_HASH

  ON load_or_support_change:
    UPDATE load_case
    UPDATE boundary_conditions
    RECOMPUTE response
    REASSESS failure_modes

  ON solver_result:
    UPDATE displacement
    UPDATE strain
    UPDATE stress
    UPDATE residual
    UPDATE convergence
    PRESERVE provenance

  ON validation_change:
    UPDATE reference_data
    RECOMPUTE validation_metrics
    UPDATE model_adequacy

# AI CONSUMPTION
AI_CONSUMPTION:
  parse_as: FORMAL_STRUCTURAL_SIMULATION_ONTOLOGY
  reasoning_mode: STRUCTURAL_MECHANICS_SIMULATION_RELATIONAL

  preserve:
    - typed_entities
    - geometry
    - material_models
    - loads
    - supports
    - boundary_conditions
    - analysis_type
    - solver_state
    - structural_results
    - failure_states
    - verification_state
    - validation_state
    - confidence
    - provenance

  infer:
    - load_path_dependencies
    - stiffness_response_dependencies
    - nonlinear_requirements
    - modal_dependencies
    - buckling_risk
    - fatigue_dependencies
    - convergence_state
    - validation_state

  prohibit:
    - invented_structural_results
    - assumed_convergence
    - assumed_material_linearity
    - assumed_failure_margin
    - assumed_validation
    - fabricated_reference_data

# FLOW HASH
FLOW_HASH_INPUT :=
  DOMAIN + ONTOLOGY + CORE_ENTITIES
  + STRUCTURAL_MODEL + GEOMETRY_MATERIAL
  + LOADS_SUPPORTS + EQUILIBRIUM
  + DISPLACEMENT_STRAIN_STRESS
  + STATIC_DYNAMIC + MODAL + BUCKLING
  + CONTACT_NONLINEARITY + PLASTICITY_THERMAL
  + FATIGUE_FAILURE + SOLVER_CONVERGENCE
  + RESULTS + DISCRETISATION
  + VERIFICATION + VALIDATION + UNCERTAINTY
  + PROVENANCE_PERFORMANCE + REASONING
  + INFERENCE_RULES + SEMANTIC_RELATIONSHIPS
  + SEMANTIC_EQUIVALENCE + CONFIDENCE
  + UPDATE_MODEL + AI_CONSUMPTION

FLOW_HASH := HASH(FLOW_HASH_INPUT)

END FLOW